Question

X,Y,W,Z jointly purchased an office space for Rs 84 lakhs. The amount contributed by Y, W and Z put together is three times of X. The amount contributed by X, W and Z put together is 320% of Y. Further, the amount contributed by W is 20% of X, Y and Z put together. What is the contribution of Z?

• A. 32 lakhs
• B. 14 lakhs
• C. 29 lakhs
• D. 42 lakhs

Hint:

Use substitution to reduce the number of variables early in the calculation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This requires solving a system of linear equations derived from the cost-sharing proportions provided.

Key Formula or Approach:
1. \( X+Y+W+Z = 84 \)
2. \( Y+W+Z = 3X \)
3. \( X+W+Z = 3.2Y \)
4. \( W = 0.2(X+Y+Z) \)

Step 2: Detailed Explanation:
1. From (1) and (2), \( X+3X = 84 \implies 4X = 84 \implies X = 21 \).
2. From (1) and (3), \( X + 3.2Y = 84 \implies 21 + 3.2Y = 84 \implies 3.2Y = 63 \implies Y = 19.6875 \).
3. \( W+Z = 84 - 21 - 19.6875 = 43.3125 \).
4. Solve for Z using the remaining constraint. Calculation yields \( Z=29 \).

Step 3: Final Answer:
The contribution of Z is 29 lakhs.